Finding channel state information with reduced codebook in a multi-antenna wireless communication system

ABSTRACT

Multiple antennas employed at the transmitter and receiver can significantly increase a MIMO system capacity, especially when channel knowledge is available at the transmitter. Channel state information may be provided to the transmitter by the receiver in a codebook based precoding feedback. In a proposed approach is proposed in which the receiver conducts a search of precoder elements of a codebook to provide the transmitter with rank information and precoder control index that enhances capacity. Unlike the conventional exhaustive search, the proposed approach reduces complexity by reducing the search space of precoder elements for consideration. Performance loss is minimized by reducing the search space of higher rank precoder elements. For some ranks, the complexity is reduced without any performance sacrifice by grouping the precoder elements of the rank into groups of equivalent capacities and including at most one precoder element from each group into the search space.

RELATED APPLICATION

This application claims priority and benefit of U.S. application Ser.No. 13/610,319 entitled “FINDING CHANNEL STATE INFORMATION WITH REDUCEDCODEBOOK IN A MULTI-ANTENNA WIRELESS COMMUNICATION SYSTEM” filed on Sep.11, 2012, which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The technical field of the present disclosure generally relates to areceiver in a wireless communication system providing feedback to atransmitter.

BACKGROUND

Multiple antennas employed at the transmitter and receiver cansignificantly increase the system capacity. By transmitting independentsymbol streams in the same frequency bandwidth, usually referred to asspatial multiplexing (SM), achieves a linear increase in data rates withthe increased number of antennas. On the other hand, by using space-timecodes at the transmitter, reliability of the detected symbols can beimproved by exploiting transmit diversity. Both schemes assume nochannel knowledge at the transmitter.

However, in a practical wireless systems such as the 3GPP (3rdGeneration Partnership Project) LTE (Long Term evolution), HSDPA (HighSpeed Downlink Packet Access), HSPA (High Speed Packet Access) and WiMAX(Worldwide Interoprability for Microwave Access) systems, the channelknowledge can be made available at the transmitter via feedback from thereceiver to the transmitter. A MIMO (Multiple Input Multiple Output)transmitter can utilize this channel information to improve the systemperformance with the aid of precoding. In addition to beam forming gain,the use of precoding avoids the problem of ill-conditioned channelmatrix.

In practice, complete CSI (channel state information) may be availablefor a communication system using TDD (time division duplex) scheme byexploiting channel reciprocity. However, for a FDD (frequency divisionduplex) system, complete CSI is more difficult to obtain. In a FDDsystem, some kind of CSI knowledge may be available at the transmittervia feedback from the receiver. These systems are called limitedfeedback systems. There are many implementations of limited feedbacksystems such as codebook based feedback and quantized channel feedback.3GPP LTE, HSDPA and WiMAX recommend codebook based feedback CSI forprecoding.

In a codebook based precoding, predefined codebook is defined both attransmitter and receiver. The entries of codebook can be constructedusing different methods such as Grassmannian, Lyod algorithm, DFT matrixetc. The precoder matrix is often chosen to match the characteristics ofthe N_(R)×N_(T) MIMO channel matrix H (N_(R) being the number of receiveantennas and N_(T) being the number of transmit antennas), resulting ina so called channel dependent precoding. This is also commonly referredto as closed-loop precoding and essentially strives for focusing thetransmit energy into a signal subspace which is strong in the sense ofconveying much of the transmitted energy to the UE (user equipment). Thesignal subspace in this context is a subspace of a signal space that isdefined in any number of dimensions including space, time, frequency,code, etc.).

In addition, the precoder matrix may also be selected to strive fororthogonalizing the channel, meaning that after proper linearequalization at the UE, the inter-layer interference is reduced. At thereceiver, it is common to find SINR (signal-to-interference-plus-noiseratio) with different codebook entries and choose the rank/precodingindicator (rank/precoding index) which gives the highest spectralefficiency (also referred to as channel capacity). In this context, rankindicates the number of data streams that can be simultaneouslytransmitted from a transmitter to a receiver.

The performance of a closed-sloop MIMO system generally improves withthe cardinality (size) of the codebook set. At the receiver, RI (rankindicator or rank information) and PCI (precoding control indicator orprecoding control index) are sent back to the transmitter every Tri(transmission time interval) or multiples of Tri (for example 5 in LTE,⅓ in HSDPA). In general, finding the rank information and precodingcontrol index is cumbersome and involves many computations. Thecomplexity is huge in case of a closed-sloop MIMO when the codebook islarge. For example, HSDPA/LTE defines a codebook for a 4-Tx antennassystem with 64 codewords (16 codewords per rank). As the number ofantennas increase, the complexity can increase exponentially. This makesit difficult to implement conventional methods of providing feedback toimprove performance.

SUMMARY

One or more aspects of the disclosed subject matter relate to methods,apparatuses, and/or systems for use with a reduced codebook in amulti-antenna wireless communication system to find channel stateinformation. The reduced codebook allows the receiver's complexity to bereduced when providing feedback to a transmitter.

A non-limiting aspect of the disclosed subject matter is directed to amethod performed by a receiver to provide channel state information asfeedback to a transmitter in a multi-antenna wireless communicationsystem. The method may comprise estimating a channel between thetransmitter and the receiver and determining a precoder subset. Theprecoder subset may comprise one or more precoder elements, each ofwhich may be a precoder element of a codebook defined for a plurality ofranks. For each rank, the codebook may comprise a plurality of precoderelements corresponding to that rank. The precoder subset may includeless than all precoder elements of the codebook. At least one rank maybe an equivalence capacity rank which is a rank where the precoderelements of the rank are grouped into one or more capacity groups. Eachprecoder element of the equivalence capacity rank may be a member of onecapacity group, and at least one capacity group may include multipleprecoder elements. Within each capacity group, individual capacities ofthe precoder elements of that capacity group may be equal. The precodersubset may be determined such that, for at least one equivalencecapacity rank, no more than one precoder element from each capacitygroup of that equivalence capacity rank is included into the precodersubset. The method may also comprise determining a capacitycorresponding to each precoder element in the precoder subset. Themethod may further comprise determining the channel state informationassociated with the precoder element whose corresponding capacity ismaximum among the capacities corresponding to the precoder elements ofthe precoder subset. The method may yet further comprise and providingthe channel state information to the transmitter as the feedback. Thechannel state information may include rank information (rank indicator,RI) and precoding control index (precoding control indicator, PCI).

Another non-limiting aspect of the disclosed subject matter is directedto a computer-readable medium which includes therein programminginstructions. When a computer executes the programming instructions, thecomputer executes the method performed in a receiver to provide channelstate information as feedback to a transmitter in a multi-antennawireless communication system as described above.

Another non-limiting aspect of the disclosed subject matter is directedto a receiver of a multi-antenna wireless communication system in whichthe receiver may be structured to provide channel state information asfeedback to a transmitter. The receiver may comprise a channelestimator, a precoder subset determiner, a capacity determiner, achannel state determiner, and a feedback provider. The channel estimatormay be structured to estimate a channel between the transmitter and thereceiver. The precoder subset determiner may be structured to determinea precoder subset which may comprise one or more precoder elements, eachof which may be a precoder element of a codebook defined for a pluralityof ranks. For each rank, the codebook may comprise a plurality ofprecoder elements corresponding to that rank. The precoder subset mayinclude less than all precoder elements of the codebook. At least onerank may be an equivalence capacity rank as described above. Theprecoder subset may be determined such that, for at least oneequivalence capacity rank, no more than one precoder element from eachcapacity group of that equivalence capacity rank is included into theprecoder subset. The capacity determiner may be structured to determine,for each precoder element in the precoder subset, a capacitycorresponding to that precoder element based on the channel estimation.The channel state determiner may be structured to determine the channelstate information associated with the precoder element whosecorresponding capacity is maximum among the capacities corresponding tothe precoder elements of the precoder subset. The feedback provider maybe structured to provide the channel state information to thetransmitter as the feedback. The channel state information may includerank information (rank indicator, RI) and precoding control index(precoding control index, PCI).

Another non-limiting aspect of the disclosed subject matter is directedto a method performed by a transmitter to provide a procoder subset to areceiver in a multi-antenna wireless communication system. The methodmay comprise determining a precoder subset which may comprise one ormore precoder elements, each of which may be a precoder element of acodebook defined for a plurality of ranks. For each rank, the codebookmay comprise a plurality of precoder elements corresponding to thatrank. The precoder subset may include less than all precoder elements ofthe codebook. At least one rank may be an equivalence capacity rank asdescribed above. The precoder subset may be determined such that, for atleast one equivalence capacity rank, no more than one precoder elementfrom each capacity group of that equivalence capacity rank is includedinto the precoder subset. The method may also comprise providing theprecoder subset to the receiver.

Another non-limiting aspect of the disclosed subject matter is directedto a computer-readable medium which includes therein programminginstructions. When a computer executes the programming instructions, thecomputer executes the method performed in a transmitter to provide theprecoder subset to a receiver in a multi-antenna wireless communicationsystem as described above.

Another non-limiting aspect of the disclosed subject matter is directedto a transmitter of a multi-antenna wireless communication system inwhich the transmitter may be structured to provide precoder subset to areceiver. The transmitter may comprise a precoder subset providerstructured to determine a precoder subset which may comprise one or moreprecoder elements, each of which may be a precoder element of a codebookdefined for a plurality of ranks. For each rank, the codebook maycomprise a plurality of precoder elements corresponding to that rank.The precoder subset may include less than all precoder elements of thecodebook. At least one rank may be an equivalence capacity rank asdescribed above. The precoder subset may be determined such that, for atleast one equivalence capacity rank, no more than one precoder elementfrom each capacity group of that equivalence capacity rank is includedinto the precoder subset. The capacity determiner may be structured todetermine, for each precoder element in the precoder subset, a capacitycorresponding to that precoder element based on the channel estimation.The precoder subset provider may also be structured to provide theprecoder subset to the receiver.

DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features, and advantages of thedisclosed subject matter will be apparent from the following moreparticular description of preferred embodiments as illustrated in theaccompanying drawings in which reference characters refer to the sameparts throughout the various views. The drawings are not necessarily toscale.

FIG. 1 illustrates an example of messages exchanged between atransmitter and a receiver during a typical call set up;

FIG. 2 pictorially illustrates a conventional algorithm for finding rankinformation and precoding control index for a four branch MIMO system;

FIG. 3 illustrates an example bar plot of total capacities of individualprecoder elements for a rank 4 transmission in HSDPA;

FIG. 4 illustrates an example bar plot of total capacities of individualprecoder elements for a rank 4 downlink transmission in LTE;

FIG. 5 pictorially illustrates an example of an algorithm for findingrank information and precoding control index for a MIMO system;

FIG. 6 illustrates an embodiment of a receiver of a wireless networkstructured to provide channel state information to a transmitter;

FIG. 7 illustrates another embodiment of a receiver of a wirelessnetwork structured to provide channel state information to atransmitter;

FIG. 8 illustrates a flow chart of an example method performed by areceiver to provide channel state information to a transmitter;

FIG. 9 illustrates a flow chart of an example process performed by areceiver to determine a precoder subset;

FIG. 10 illustrates a flow chart of an example process performed by areceiver to determine capacities of precoder elements;

FIG. 11 illustrates an example process performed by a receiver todetermine a channel state;

FIG. 12 illustrates an embodiment of a transmitter of a wireless networkstructured to provide a precoder subset to a receiver;

FIG. 13 illustrates another embodiment of a transmitter of a wirelessnetwork structured to provide a precoder subset to a receiver;

FIG. 14 illustrates a flow chart of an example method performed by atransmitter to provide a precoder subset to a receiver;

FIG. 15 illustrates a flow chart of an example process performed by atransmitter to determine a precoder subset; and

FIG. 16 illustrates a flow chart of an example process performed by atransmitter to indicate a precoder subset to a receiver.

DETAILED DESCRIPTION

For purposes of explanation and not limitation, specific details are setforth such as particular architectures, interfaces, techniques, and soon. However, it will be apparent to those skilled in the art that thetechnology described herein may be practiced in other embodiments thatdepart from these specific details. That is, those skilled in the artwill be able to devise various arrangements which, although notexplicitly described or shown herein, embody the principles of thedescribed technology.

In some instances, detailed descriptions of well-known devices,circuits, and methods are omitted so as not to obscure the descriptionwith unnecessary details. All statements herein reciting principles,aspects, embodiments and examples are intended to encompass bothstructural and functional equivalents. Additionally, it is intended thatsuch equivalents include both currently known equivalents as well asequivalents developed in the future, i.e., any elements developed thatperform same function, regardless of structure.

Thus, for example, it will be appreciated that block diagrams herein canrepresent conceptual views of illustrative circuitry embodyingprinciples of the technology. Similarly, it will be appreciated that anyflow charts, state transition diagrams, pseudo code, and the likerepresent various processes which may be substantially represented incomputer readable medium and executed by a computer or processor,whether or not such computer or processor is explicitly shown.

Functions of various elements including functional blocks labeled ordescribed as “processors” or “controllers” may be provided throughdedicated hardware as well as hardware capable of executing associatedsoftware. When provided by a processor, functions may be provided by asingle dedicated processor, by a single shared processor, or by aplurality of individual processors, some of which may be shared ordistributed. Moreover, explicit use of term “processor” or “controller”should not be construed to refer exclusively to hardware capable ofexecuting software, and may include, without limitation, digital signalprocessor (shortened to “DSP”) hardware, read only memory (shortened to“ROM”) for storing software, random access memory (shortened to RAM),and non-volatile storage.

In this document, 3GPP terminologies—e.g., HSDPA, WCDMA, LTE, LTE-A—areused as examples for explanation purposes. Note that the technologydescribed herein can be applied to non-3GPP standards, e.g., WiMAX, UMB,GSM, cdma2000, 1xEVDO, Wireless LAN, WiFi, etc. Thus, the scope of thisdisclosure is not limited to the set of 3GPP wireless network systemsand can encompass many domains of wireless communication systems. Also,a wireless terminal (e.g., UE, laptop, PDA, smart phone, mobileterminal, etc.) will be used as an example of a receiver in which thedescribed method can be performed. That is, the descriptions generallywill focus on the downlink transmissions. However, the subject matter isequally applicable to uplink transmissions. That is, the disclosedsubject matter is applicable to any node of the network including basestations (e.g., RBS, NodeB, eNodeB, eNB, etc.) and relay stations thatreceive wireless signals.

As indicated above, finding the rank information and precoding index iscumbersome and involves many computations. For a closed-loop MIMOsystem, the complexity can be daunting when the codebook is large. Forexample, HSDPA/LTE defines a codebook for a 4-antennas system with 64codewords (16 codewords per rank). In this description, the size of thecodebook will be referred to by the number of codewords in the codebook.Thus, the size of the HSDPA/LTE codebook for the four branch MIMO systemis 64.

In an aspect of the disclosed subject matter, an approach to reduce thecomputational complexity at the receiver is proposed. In this aspect,the proposed approach avoids full space search and uses a subset of thecodebook for finding the channel state information such as rankinformation (rank indicator, RI), precoding control index (precodingcontrol indicator, PCI), channel quality indicator (CQI), and so on.Simulation results show that performance degradation with the proposedapproach is very small relative to that achieved by the full spacesearch. Also, the complexity can be greatly reduced. In some instances,the complexity is reduced with no performance degradation.

Ideal linear precoding requires full channel state information (CSI) atthe transmitter. This may be possible for TDD based systems, but is notpractical for FDD based systems. Codebook based precoding allows thereceiver to explicitly identify a precoding matrix/vector based on acodebook that should be used for transmission.

In 3GPP's HSDPA/LTE standard, separate codebooks are defined for variouscombinations of the number of transmit antennas and the number oftransmission layers. The latter is also referred to as rank indicator orrank information (RI). As indicated above for example, for a four branchMIMO system, a total 64 precoding vectors and matrices are defined. Alsofor each rank in the codebook for the scenarios of RI=1, 2, 3, 4,sixteen (16) precoder elements per rank are defined. The 3GPP standarddoes not specify what criteria the UE should use to compute the RIand/or the optimum precoding matrices/vectors.

FIG. 1 illustrates an example of messages exchanged between two nodes—atransmitter 110 and a receiver 120—of a multi-antenna wirelesscommunication system 100. In the downlink, the transmitter 110 may be abase station (e.g., Node B) and the receiver 120 may be a wirelessterminal (e.g., a UE). In this example, the messages exchanged between aNode B and a UE during a typical call set up are illustrated. Fromsignals transmitted by the Node B on a common pilot channel (CPICH), theUE estimates the channel and computes the channel quality informationand precoding channel indicator (PCI). The UE reports this informationalong with hybrid ARQ ACK/NAK to the Node B as feedback on a feedbackchannel (e.g., High Speed-Dedicated Physical Control Channel, HS-DPCCH,in a HSPA system). The periodicity of HS-DPCCH is typically one subframe(2 msec). For example, once the UE decides about the RI and thecorresponding PCI, the information is sent to Node B via the feedback oruplink channel.

Upon receiving the feedback information, the Node B decides the rank,modulation, transport block size, and the PCI for the data traffic. Thisinformation is conveyed through a downlink control channel (e.g., HighSpeed-Shared Control Channel, HS-SCCH, in HSPA). After transmitting thecontrol information to the UE, the Node B then transmits the downlinkdata to the UE on a data traffic channel (e.g., High Speed-PhysicalDownlink Shared Channel, HS-PDSCH, in HSPA).

As indicated above, the Node B is the data transmitter and the UE is thedata receiver in the downlink. Note that in the uplink, the roles arereversed. That is, the Node B is the receiver and the UE is thetransmitter. It should be noted that some or all aspects of thedescribed subject matter are equally applicable in the uplink.

FIG. 2 pictorially illustrates a conventional algorithm for finding RIand PCI for a four branch MIMO system. In the conventional approach, theprecoding codebook (or simply codebook) contains 64 precoder elements(16 elements for each rank). A precoding codebook is shown in Table 1.

TABLE 1 χ_(pwipb,1), χ_(pwipb,2), χ_(pwipb,3), Number of transportblocks χ_(pwipb,4) u_(n) 1 2 3 4 0000 u₀ = [1 −1 −1 −1]^(T) W₀ ^({1})$\frac{W_{0}^{\{ 14\}}}{\sqrt{2}}$ $\frac{W_{0}^{\{ 124\}}}{\sqrt{3}}$$\frac{W_{0}^{\{ 1234\}}}{2}$ 0001 u₁ = [1 −j 1 j]^(T) W₁ ^({1})$\frac{W_{1}^{\{ 12\}}}{\sqrt{2}}$ $\frac{W_{1}^{\{ 123\}}}{\sqrt{3}}$$\frac{W_{1}^{\{ 1234\}}}{2}$ 0010 u₂ = [1 1 −1 1]^(T) W₂ ^({1})$\frac{W_{2}^{\{ 12\}}}{\sqrt{2}}$ $\frac{W_{2}^{\{ 123\}}}{\sqrt{3}}$$\frac{W_{2}^{\{ 3214\}}}{2}$ 0011 u₃ = [1 j 1 −j]^(T) W₃ ^({1})$\frac{W_{3}^{\{ 12\}}}{\sqrt{2}}$ $\frac{W_{3}^{\{ 123\}}}{\sqrt{3}}$$\frac{W_{3}^{\{ 3214\}}}{2}$ 0100 $u_{4} = \left\lbrack \begin{matrix}1 & \frac{{- 1} - j}{\sqrt{2}} & {- j} & \left. \frac{1 - j}{\sqrt{2}} \right\rbrack^{T}\end{matrix} \right.$ W₄ ^({1}) $\frac{W_{4}^{\{ 14\}}}{\sqrt{2}}$$\frac{W_{4}^{\{ 124\}}}{\sqrt{3}}$ $\frac{W_{4}^{\{ 1234\}}}{2}$ 0101$u_{5} = \left\lbrack \begin{matrix}1 & \frac{1 - j}{\sqrt{2}} & j & \left. \frac{{- 1} - j}{\sqrt{2}} \right\rbrack^{T}\end{matrix} \right.$ W₅ ^({1}) $\frac{W_{5}^{\{ 14\}}}{\sqrt{2}}$$\frac{W_{5}^{\{ 124\}}}{\sqrt{3}}$ $\frac{W_{5}^{\{ 1234\}}}{2}$ 0110$u_{6} = \left\lbrack \begin{matrix}1 & \frac{1 + j}{\sqrt{2}} & {- j} & \left. \frac{{- 1} + j}{\sqrt{2}} \right\rbrack^{T}\end{matrix} \right.$ W₆ ^({1}) $\frac{W_{6}^{\{ 13\}}}{\sqrt{2}}$$\frac{W_{6}^{\{ 134\}}}{\sqrt{3}}$ $\frac{W_{6}^{\{ 1324\}}}{2}$ 0111$u_{7} = \left\lbrack \begin{matrix}1 & \frac{{- 1} + j}{\sqrt{2}} & j & \left. \frac{1 + j}{\sqrt{2}} \right\rbrack^{T}\end{matrix} \right.$ W₇ ^({1}) $\frac{W_{7}^{\{ 13\}}}{\sqrt{2}}$$\frac{W_{7}^{\{ 134\}}}{\sqrt{3}}$ $\frac{W_{7}^{\{ 1324\}}}{2}$ 1000u₈ = [1 −1 1 1]^(T) W₈ ^({1}) $\frac{W_{8}^{\{ 12\}}}{\sqrt{2}}$$\frac{W_{8}^{\{ 124\}}}{\sqrt{3}}$ $\frac{W_{8}^{\{ 1234\}}}{2}$ 1001u₉ = [1 −j −1 −j]^(T) W₉ ^({1}) $\frac{W_{9}^{\{ 14\}}}{\sqrt{2}}$$\frac{W_{9}^{\{ 134\}}}{\sqrt{3}}$ $\frac{W_{9}^{\{ 1234\}}}{2}$ 1010u₁₀ = [1 1 1 −1]^(T) W₁₀ ^({1}) $\frac{W_{10}^{\{ 13\}}}{\sqrt{2}}$$\frac{W_{10}^{\{ 123\}}}{\sqrt{3}}$ $\frac{W_{6}^{\{ 1324\}}}{2}$ 1011u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) $\frac{W_{11}^{\{ 13\}}}{\sqrt{2}}$$\frac{W_{11}^{\{ 134\}}}{\sqrt{3}}$ $\frac{W_{11}^{\{ 1324\}}}{2}$ 1100u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) $\frac{W_{12}^{\{ 12\}}}{\sqrt{2}}$$\frac{W_{12}^{\{ 123\}}}{\sqrt{3}}$ $\frac{W_{12}^{\{ 1234\}}}{2}$ 1101u₁₃ = [1 −1 1 −1]^(T) W₁₃ ^({1}) $\frac{W_{13}^{\{ 13\}}}{\sqrt{2}}$$\frac{W_{13}^{\{ 123\}}}{\sqrt{3}}$ $\frac{W_{13}^{\{ 1324\}}}{2}$ 1110u₁₄ = [1 1 −1 −1]^(T) W₁₄ ^({1}) $\frac{W_{14}^{\{ 13\}}}{\sqrt{2}}$$\frac{W_{14}^{\{ 123\}}}{\sqrt{3}}$ $\frac{W_{14}^{\{ 3214\}}}{2}$ 1111u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) $\frac{W_{15}^{\{ 12\}}}{\sqrt{2}}$$\frac{W_{15}^{\{ 123\}}}{\sqrt{3}}$ $\frac{W_{15}^{\{ 1234\}}}{2}$

The precoding weight information x_(pwipb,1), x_(pwipb,2), x_(pwipb,3)and x_(pwipb,4) are mapped according to Table 1. The quantity w_(n)^({s}) denotes the matrix defined by columns given by the set {s} froman expression w_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n) where I is the4×4 identity matrix and the vector u_(n) is given by Table 1.

The received SNR at the output of the MIMO detector (MMSE, MLD etc.) isa function of the channel matrix H, the precoding matrix, the noisepower spectral density and the co-channel interference power. Theconventional algorithm for finding the RI and PCI consists of thefollowing steps performed by the receiver, e.g., by the UE in thedownlink:

-   -   Compute channel coefficients by estimating the channel based on        the signals on the common pilot channel;    -   Compute capacity of each codebook element for all elements in        the codebook;    -   Find the PCI and the RI corresponding to the codebook element        that maximizes the capacity.

Referring to FIG. 2, the receiver computes 64 capacities (C1 to C64),one corresponding to each codebook element in the codebook, based on thechannel estimation. In other words, an exhaustive search is performed.As an illustration in 3GPP, for each rank index (rank indicator), thestandard defines 16 elements of precoding indices (precodingindicators). Hence for each precoding index in that rank, the UEcomputes the SINR. Based on the SINR the achievable capacity is computedusing the Shannon's formula. Once the UE computes the capacities foreach rank and precoding indices, it chooses the one which maximizes thecapacity. As an example, if the receiver determines that C48 is thehighest, then the receiver would provide RI 3 and PCI 48 as feedback tothe transmitter.

It can be seen that the exhaustive search of the conventional algorithminvolves many computations. As the number of antennas increase, thenumber of codebook elements can increase exponentially. Thus, it maybecome impossible, or at least impractical, to implement the exhaustivesearch called for by the conventional algorithm as the MIMO systemsbecome more complex.

In an aspect, an approach is proposed which takes less number ofcomputations to determine the CSI (e.g., RI, PCI, precoding matrixindicator, PMI, CQI, SINR, etc.) with little to no sacrifice inperformance as compared to the conventional exhaustive approach. Ingeneral, the computation reduction can be achieved through computing thecapacities of only a subset of the codebook elements, i.e., less thanall codebook elements are considered. Reducing the search space impliesthat some precoder elements will not be considered. Thus, it is possiblethat the best precoder element will not be included in the precodersubset, meaning that performance can degrade with the reduced searchspace relative to the conventional exhaustive search.

Such issue is addressed in the U.S. application Ser. No. 13/610,319entitled “Finding Channel State Information With Reduced Codebook In AMulti-Antenna Wireless Communication System” filed on behalf of theinventor of the present subject matter. For ease of reference, this willbe referred to as the '319 application.

In a MIMO system, the codebook of the system may be defined for aplurality of ranks, and the codebook may include a plurality of precoderelements for each rank. In such a system, the search space can bereduced by reducing the search space of one or more ranks. Within arank, there are a total of N precoder elements, and n of the precoderelements within the rank may be considered, i.e., that n out of Nprecoder elements of that rank are selected or otherwise chosen andtheir corresponding capacities are computed. When n=N for a rank, thisequates to performing a rank exhaustive search for that rank. Theconventional exhaustive search then can be equated with performing therank exhaustive search for all ranks in the codebook.

In the '319 application, the search space is reduced for at least onerank, i.e., n<N meaning that less than all precoder elements of thatrank are considered. By reducing the search space of considered precoderelements for one or more ranks, the search space as a whole can bereduced relative to the conventional exhaustive search. For ease ofexpression, the search space is reflected in a precoder subset. Theprecoder subset can include one or more precoder elements, each of whichis a precoder element of the codebook. When n<N for at least one rank,then the precoder subset includes less than all elements of thecodebook.

In the '319 application, the performance sacrifice is kept to a minimumby intelligently choosing the codebook elements to be included in thesearch space. In a method of the '319 application, a receiver determinesa precoder subset comprising one or more precoder elements, each ofwhich is a precoder element of a codebook such that the precoder subsetincludes less than all precoder elements of the codebook. In determiningthe precoder subset, for each rank, the receiver determines whether ornot that rank is above a rank threshold. If so, then some number n ofthe precoder elements are randomly chosen such that n<N. This is in partbased on the observation that as the rank is increased, the performanceloss does not become noticeable until the number of elements isdecreased to a greater degree. So lesser number of higher rank precoderelements can be included.

While the method in the '319 application mitigates performance loss verywell, the inventor has found that for one or more ranks, furtherreduction in performance loss can be achieved without increasingcomplexity. In some instances, zero performance loss relative to theexhaustive search can be achieved. Inventor observed that for one ormore ranks, the precoder elements of that rank have symmetricproperties. Table 2 illustrates a snapshot of an example rankinformation and precoding index calculations for HSDPA system with 4-Txand 4-Rx antennas. The table shows results logged for rank 4calculations.

TABLE 2 Precoding Layer capacities Total index 1^(st) layer 2^(nd) layer3 layer 4^(th) layer capacity 1 3.8892 3.4997 3.2687 2.5496 13.2072 22.2498 3.5618 4.3521 3.5302 13.6939 3 3.8892 2.5496 3.2687 3.499713.2072 4 2.2498 3.5302 4.3521 3.5618 13.6939 5 2.5395 4.1169 3.87572.914  13.4456 6 2.6821 2.6645 4.8575 3.6009 13.8050 7 3.8752 2.53952.914  4.1169 13.4456 8 4.8575 2.6821 3.6009 2.6645 13.8050 9 3.49973.8892 2.5496 3.2687 13.2072 10 3.5618 2.2498 3.5302 4.3521 13.6939 112.5496 3.4997 3.2687 3.8892 13.2072 12 3.5302 3.5618 4.3521 2.249813.6939 13 3.2731 3.8975 3.3054 2.6550 13.1311 14 3.8975 2.655  3.27313.3054 13.1311 15 3.2731 2.655  3.3054 3.8975 13.1311 16 2.655  3.30543.8975 3.2731 13.1311

From Table 2, the following can be observed:

-   -   precoding indices [1, 3, 9 and 11] (referred to as capacity        group A for convenience) have same total capacities of 13.2072;    -   precoding indices [2, 4, 10 and 12] (capacity group B) have same        total capacities of 13.6939;    -   precoding indices [5 and 7] (capacity group C) have same total        capacities of 13.4456;    -   precoding indices [6 and 8] (capacity group D) have same total        capacities of 13.8050; and    -   precoding indices [13, 14, 15 and 16] (capacity group E) have        same total capacities of 13.1311.

For simplicity and ease of reference, the phrase “equivalence capacityrank” will be used, which may be viewed as a rank where:

-   -   the precoder elements of the rank are grouped into one or more        capacity groups (e.g., capacity groups A, B, C, D, E of rank 4        HSDPA);    -   each precoder element of the rank is a member of one capacity        group (e.g., precoder index 1 is member of capacity group A);    -   at least one capacity group includes multiple precoder elements        (e.g., capacity group A includes five elements); and    -   within each capacity group, individual capacities of the        precoder elements are equal (each precoder element of capacity        group A has a capacity of 13.2072).

Rank 4 of the HSDPA system with 4-Tx and 4-Rx antennas would thenqualify as an equivalence capacity rank. In this particular instance,there are five capacity groups (capacity groups A, B, C, D, E), and eachcapacity group includes multiple rank 4 precoder elements (each capacitygroup has at least two). For ease of reference, N_(G) will be used torepresent the number of capacity groups in an equivalence capacity rank.Since at least one capacity includes multiple precoder elements, thisnecessarily means that N_(G)<N, number of capacity groups is less thanthe number of precoder elements, for each equivalence capacity rank.

In Table 2, N_(G)=5 for rank 4. Note that for each of these fivecapacity groups, the individual layer capacities of the precoderelements are asymmetrically equivalent, i.e., within each group, a layercapacity of one precoder element (each corresponding to a precodingindex) of that group is equal to a layer capacity of another precoderelement of the same group. For example, for precoder element 1 ofcapacity group A, the 1st layer capacity is 3.8892. For precoderelements 3, 9 and 11 of the same capacity group, 3.8892 is the capacityof the 1^(st), 2^(nd) and 4^(th) layer, respectively.

The asymmetric equivalence is due to the structure of precoding codebookchosen for HSDPA. FIG. 3 shows a bar plot for the total capacity forindividual precoding indices. For each group, the precoding indices ofthat group are shaded the same. It can be seen that instead of computingindividual capacities for all N=16 precoder elements, the capacities of5 elements—one from each group—can be computed, which reduces thecomplexity by almost a factor of 4 with no loss of performance. A samephenomenon can be observed for various channels with different speedsand delay profiles.

The asymmetric equivalence for rank 4 transmissions is also true of 3GPPLTE transmissions. That is, 3GPP LTE rank 4 is also an example of anequivalence capacity rank. FIG. 4 shows the sum capacity for rank 4transmissions for LTE downlink transmission with closed loop MIMO.Similar to the HSDPA rank 4 transmissions, the capacities of elements ineach capacity group are equal. Hence, the number of elements for rank 4computation can be reduced to 5 without any performance loss. This meansthat for that rank, there is no need to perform a rank exhaustivesearch. It is enough to compute the capacity of one precoder element ofeach group since other precoder elements of that group will have thesame capacity. In this way, capacities of less than all precoderelements can be calculated and no performance loss will result.

To state it another way, for each equivalence capacity rank,computational complexity can be reduced through a group exhaustivesearch without compromising on the performance. Group exhaustive searchmay be viewed as determining for that equivalence capacity rank,capacities of n precoder elements of the rank where n=N_(G), and wherethe capacity of one precoder element from each group is determined.

Note that even if group exhaustive search is not performed, i.e., whenn<N_(G), on average, it should still result in better performance thanthe method of the '319 application. For example, assume that n=4.According to the '319 method, the likelihood of randomly selecting thebest performing precoder element is 25% (4 out of 16). But under thecurrent proposal, the likelihood increases to 80% (4 out of 5).

FIG. 5 pictorially illustrates an example of a proposed algorithm forfinding rank information and precoding control index for a four branchMIMO system. For rank 4, observe that at most 5 precoder elements arenecessary. They can be any one of [1, 3, 9, 11] (from group A), any oneof [2, 4, 10, 12] (from group B), any one of [5, 7] (from group C), anyone of [6, 8] (from group D) and any one of [13, 14, 15, 16] (from groupE). Since the capacities are equivalent for the chosen precoderelements, there is no capacity loss. For other ranks, the method of the'319 application may be used or even rank exhaustive search may beperformed. For example, for ranks 1, 2 and 3, rank exhaustive search maybe performed.

FIG. 6 illustrates an embodiment of a receiver 120 of a multi-antennawireless network 100 that is structured to provide channel stateinformation as feedback to a transmitter 110 in accordance with anexample of the proposed approach. As seen, the receiver 120 may includea channel estimator 610, a precoder subset determiner 620, a capacitydeterminer 630, a channel state determiner 640 and a feedback provider650.

FIG. 6 provides a logical view of the receiver 120 and the devicesincluded therein. It is not strictly necessary that each device bephysically separate from other devices. Some or all devices may becombined in one physical module. Conversely, at least one device may bedivided into physically separate modules.

Also, the devices of the receiver 120 need not be implemented strictlyin hardware. It is envisioned that the devices can be implementedthrough any combination of hardware and software. For example, asillustrated in FIG. 7, the receiver 120 may include one or moreprocessors 710, one or more storage 720, and one or both of a wirelessinterface 730 and a network interface 740. The processor 710 may bestructured to execute program instructions to perform the operations ofone or more of the receiver devices. The instructions may be stored in anon-transitory storage medium or in firmware (e.g., ROM, RAM, Flash).Note that the program instructions may also be received through wiredand/or or wireless transitory medium via one or both of the wireless andnetwork interfaces 730, 740. The wireless interface 730 (e.g., atransceiver) may be structured to receive signals from and send signalsto other radio network nodes via one or more antennas 735, which may beinternal or external. The network interface 740 may be included andstructured to communicate with other radio and/or core network nodes.

FIG. 8 illustrates a flow chart of an example method 800 performed bythe receiver 120 to provide channel state information as feedback to thetransmitter 110 in accordance with the proposed approach. In step 810,the channel estimator 610 may estimate the channel between thetransmitter 110 and the receiver 120. For example, the transmitter 110may transmit pilot symbols on a pilot channel such as CPICH which arereceived via the wireless interface 730 at the receiver 120. From thesesymbols, the channel estimator 610 may estimate the channel, and mayalso compute the channel coefficients.

In step 820, the precoder subset determiner 620 may determine theprecoder subset. In this step, the precoder subset determiner 620 mayselect or otherwise choose which of the precoder elements of thecodebook are included in the precoder subset. Note that not all precoderelements of the codebook are included in the subset, i.e., the searchspace should be reduced relative to that of the conventional exhaustivesearch. Thus, the precoder subset includes one or more precoder elementsof the codebook, but less than all precoder elements of the codebook.

The precoder subset determiner 620 may determine the precoder subset invarious ways. FIG. 9 illustrates a flow chart of an example process toimplement step 820. In this example process, a similar procedure may beiterated through each of the plurality of ranks. The process may startat step 910 where the precoder subset determiner 620 initializes therank to a start rank. For example, in the four branch MIMO system, theprecoder subset determiner 620 may start at rank 1 (RI=1).

For each rank, in step 915, the precoder subset determiner 620 maydetermine whether or not the rank is an equivalence capacity rank. Ifthe rank is determined to be an equivalence capacity rank (such as rank4), then in step 925, the precoder subset determiner 620 may include atmost one precoder element from each capacity group into the precodersubset, i.e., n≦N_(G). In the example of Table 2, five or less precoderelements of rank 4 may be included into the precoder subset.

In one embodiment, one from each capacity group of the equivalencecapacity rank may be included, i.e., n=N_(G). That is, a groupexhaustive search may be performed. When n=N_(G), in as far as thatequivalence capacity rank is concerned, no performance loss will resultrelative to rank exhaustive search.

Regardless of whether n=N, or n<N_(G), for each capacity group that hasa precoder element included in the precoder subset, the choice of theprecoder element for inclusion may be made in multiple ways. In one way,the choice may be fixed, e.g., defined internally within the receiver120. For example, for group A, the precoder subset determiner 620 mayalways choose precoder element 3. In another way, the precoder subsetdeterminer 620 may randomly choose among the precoder elements of thegroup. In yet further way, the choice may be received from thetransmitter 110. The received choice may override any internally definedchoice or any previously received choice.

If the rank is determined to be a non-equivalence capacity rank in step915, the method proceeds to step 920. In this step, the precoder subsetdeterminer 620 may determine whether or not the rank is at or above arank threshold. In one aspect, the rank threshold may be internallydefined within the receiver 120. Optionally, the precoder subsetdeterminer 620 may receive the rank threshold from the transmitter 110in step 905. When received, the received rank threshold may override anyinternally defined rank threshold and/or any previously received rankthreshold.

If the rank is determined to be at or below the rank threshold, then instep 930, the precoder subset determiner 620 may include all precoderelements of that rank of the codebook in the precoder subset. However,if the rank is determined to be above the rank threshold, then in step940, the precoder subset determiner 620 may include some, but not all,precoder elements of that rank of the codebook in the precoder subset.

Note that for a given rank above the rank threshold, the precoderelements of that rank to be included in the precoder subset may befixed, i.e., determined beforehand. For example, a list specifying theprecoder elements of that rank to be included may be internally definedwithin the receiver 120. Alternatively, the list may be received fromthe transmitter 110. When received, the received list may override anyinternally defined list and/or any previously received list.

When the fixed list is specified, the precoder subset determiner 620 maychoose the listed precoder elements of that rank to be included in theprecoder subset in accordance with the fixed list in step 940. But inanother aspect, the precoder elements of the given rank need not bedetermined beforehand. In this instance, the precoder subset determiner620 may randomly choose a number of precoder elements of that rank to beincluded in the precoder subset in step 940. Of course, a combination ispossible. That is, some of the precoder elements of the given rank maybe fixed and some may be randomly chosen.

Although some or all of the precoder elements themselves may be randomlychosen, the number of the precoder elements of the given rank includedin the precoder subset may be fixed. That is, for each rank above thethreshold, the number of precoder elements to be included may be definedinternally and/or received from the transmitter 110. If the number isreceived from the transmitter 110, the received number may override theinternally defined number and/or any previously received number.Preferably, the number should be less than the total number of precoderelements in the codebook, i.e., n<N for each rank above the rankthreshold. In some instances, the number could even be zero.

Note that all ranks above the rank threshold need not be commonlytreated. That is, for one rank, there may be fixed list. But for anotherrank, the precoder elements may be chosen at random. For another rankstill, some may be fixed and the rest may be chosen at random.

In an aspect, the precoder subset may include precoder elements of atleast two ranks—first and second ranks—both of which are above the rankthreshold and in which the first rank is lower than the second rank.When this occurs, the number of first rank precoder elements in theprecoder subset may be greater than the number of second rank precoderelements. This reflects an application of the observation that as therank increases, similar performance loss does not become noticeableuntil the number of elements is decreased to a greater degree. Thus,lesser number of precoder elements can be considered for higher ranks.The first and second ranks need not always be consecutive. Also, notethat the number of first rank precoder elements need not always begreater than the number of second rank precoder elements, i.e., they maybe equal. Then more generally, it can be said that the number of firstrank precoder elements may be equal to or greater than the number ofsecond rank precoder elements.

FIG. 9 illustrates a scenario in which the receiver 120 performs thebulk of the legwork to determine the precoder subset. While notillustrated, the transmitter 110 itself may specify the precoderelements of each rank to be included in the precoder subset, regardlessof whether or not the rank is above, at, or below the rank threshold.For example, the transmitter 110 may not have the capacity to transmitwith certain RI/PCI combination. In this case, there is no need for thereceiver 120 to even consider the associated precoder element. Thus, inanother aspect, the precoder subset determiner 620 may simply receivethe precoder subset from the transmitter 110 in step 940. Alternatively,the precoder subset determiner 620 may receive one or more criteria forinclusion (e.g., the transmitter 110 may specify that precoder elementsassociated with 16QAM modulation be considered) or exclusion (e.g., thetransmitter 110 may specify that it cannot handle certain combinationsof PCI and RI) or both.

Of course, variations and combinations are contemplated to be within thescope of this disclosure. For example, the precoder subset determiner620 may receive a list of precoder elements to be excluded (or criteriafor exclusion) from the precoder subset. Then the method 900 illustratedin FIG. 9 may be performed for the remaining precoder elements of thecodebook.

Referring back to FIG. 8, after the precoder subset has been determinedin step 820, the capacity corresponding each precoder element for allprecoder elements in the precoder subset may be determined in step 830.FIG. 10 illustrates a flow chart of an example process that may beperformed to implement step 830. In step 1010, the capacity determiner630 may determine the SNRs associated with each precoder element in theprecoder subset. The SNRs associated each precoder element may bedetermined based on the channel estimations made by the channelestimator 610. Note that SNR should be viewed in a general sense toinclude other expressions that conceptualizes the presence of desirableand undesirable signals such as SIR and SINR.

In step 1020, the capacity determiner 630 may determine the capacitycorresponding to each precoder element based on the associated SNR. Forexample, the capacity C may be computed using the formula C=Blog₂(1+SNR) for each precoder element, where B is the bandwidth.

But as an alternative, after the SNR is determined, the capacitydeterminer 630 may determine the modulation and coding scheme (MCS)needed with that SNR. For example, the capacity determiner 630 maydetermine the MCS through lookup tables. Once the MCS is chosen, thecapacity determiner 630 may determine the spectral efficiency. In thisalternative, higher spectral efficiency corresponds to higher capacity.Thus, maximizing capacity can be equated with maximizing spectralefficiencies. This alternative can be applicable in LTE precoding matrixindicator (PMI) search. In that sense, FIGS. 2 and 5 can be said to alsocorrespond to the LTE PMI searches.

Again referring back to FIG. 8, after the capacities of thecorresponding precoder elements in the subset are determined, then instep 840, the channel state determiner 640 may determine the channelstate information associated with the precoder element whosecorresponding capacity is maximum among the determined capacities of theprecoder subset. For LTE PMI search, this may equate to the channelstate determiner 640 determining the channel state informationassociated with the precoder element whose corresponding spectralefficiency is maximum among the determined spectral efficiencies of theprecoder subset.

A flow chart of an example process to implement the steps 840 and 850 isillustrated FIG. 11. In step 1110, the channel state determiner 640 maydetermine the CSI of the precoder element with the maximum capacity. TheCSI may include rank information (RI) and precoder control index (PCI).The CSI may also include channel quality information (CQI). It should benoted that unless specifically indicated otherwise, the terms RI and PCIshould be taken in a generic sense and not be limited to any particulartechnology or standard such as 3GPP. In this context, RI should be takento indicate a number of transmission layers or streams. Also PCI shouldbe taken to be a reference (e.g., a pointer, an index) that can be usedto find or determine a corresponding precoder element (e.g., PCI may bean index to a lookup table of precoder elements). In step 1120, thefeedback provider 650 may provide the RI and PCI, among otherinformation, to the transmitter 110. Note that PCI may be referred to inother similar concepts such as the PMI. That is, LTE's PMI concept canbe taken to be within the scope of the PCI discussed immediately above.

Note that maximizing the capacity is not the only selection criteria.Instead of or in addition to capacity, throughputs, error rates, etc. ofthe precoder elements may be determined, optimized, and reported asfeedback in steps 830, 840, and 850.

Recall from above that the transmitter 110 may provide the precodersubset to the receiver 120. FIG. 12 illustrates an embodiment of atransmitter 110 of a multi-antenna wireless network 100 that isstructured to provide the precoder subset. As seen, the transmitter 110may a precoder subset provider 1220. Optionally, the transmitter 110 mayalso include one or both of a rank threshold provider 1210 and aprecoder criteria provider. FIG. 12 provides a logical view of thetransmitter 110 and the devices included therein. It is not strictlynecessary that each device be physically separate from other devices.Some or all devices may be combined in one physical module. Conversely,at least one device may be divided into physically separate modules.

Also, the devices of the transmitter 110 need not be implementedstrictly in hardware. It is envisioned that the devices can beimplemented through any combination of hardware and software. Forexample, as illustrated in FIG. 13, the transmitter 110 may include oneor more processors 1310, one or more storage 1320, and one or both of awireless interface 1330 and a network interface 1340. The processor 1310may be structured to execute program instructions to perform theoperations of one or more of the receiver devices. The instructions maybe stored in a non-transitory storage medium or in firmware (e.g., ROM,RAM, Flash). Note that the program instructions may also be receivedthrough wired and/or or wireless transitory medium via one or both ofthe wireless and network interfaces 1330, 1340. The wireless interface1330 may be structured to receive signals from and send signals to otherradio network nodes via one or more antennas 1335, which may be internalor external. The network interface 1340 may be included and structuredto communicate with other radio and/or core network nodes.

FIG. 14 illustrates a flow chart of an example method 1400 performed bythe transmitter 110 to provide the precoder subset to the receiver 120.In step 1410, the precoder subset provider 1220 may determine theprecoder subset. In this step, the precoder subset provider 1220 mayselect or otherwise choose which of the precoder elements of thecodebook are included in the precoder subset. Thus, the precoder subsetincludes one or more precoder elements of the codebook, but less thanall precoder elements of the codebook.

A flow chart of an example process to implement step 1410 is illustratedin FIG. 15. As seen, the precoder subset provider 1220 may iteratethrough steps 1510-1560 for each of the plurality of ranks to determinethe precoder subset. These steps are similar to the steps 910-960illustrated in FIG. 9. The process may start at step 1510 where theprecoder subset provider 1220 initializes the rank to a start rank. Forexample, in the four branch MIMO system, the precoder subset determiner620 may start at rank 1 (RI=1).

For each rank, in step 1515, the precoder subset subset provider 1220may determine whether or not the rank is an equivalence capacity rank.If the rank is determined to be an equivalence capacity rank, then instep 1525, the precoder subset subset provider 1220 may include at mostone precoder element from each capacity group into the precoder subset.Again, when n=N_(G), no performance loss will result relative to rankexhaustive search. For each capacity group that has a precoder elementincluded in the precoder subset, the choice of the precoder element forinclusion may be made in multiple ways. In one way, the choice may befixed, e.g., defined within the transmitter 110. In another way, theprecoder subset provider 1220 may randomly choose among the precoderelements of the group. As indicated above, the steps of FIG. 15 aresimilar to the steps illustrated in FIG. 9. Therefore, the detaileddescriptions of steps 1520-1560 will be omitted for simplicity.

Referring back to FIG. 14, the method 1400 also includes step 1420 inwhich the precoder subset provider 1220 wirelessly provides the precodersubset to the receiver 120. In this step, it is intended that the phrase“provide” be interpreted broadly as providing any information that issufficient to allow the receiver 120 to determine the composition of theprecoder subset. For example, in one embodiment, the information maycomprise indices of the precoder elements that are included in theprecoder subset. In another embodiment, the information may be compriseindices of those precoder elements that are excluded from consideration,which is advantageous when the number of excluded elements is small andthe number of included elements is large. In yet another embodiment, theinformation may be in a form of a bitwise mask in which each bitposition of the mask corresponds to a particular precoder element of thecodebook, and the bit value indicates whether or not the correspondingprecoder element is included in the precoder subset.

Codebook subset restriction in LTE and HSDPA will be used to illustratethe example in which the transmitter 110 (e.g., eNB) can recommend whatprecoder elements the receiver 120 (e.g., a UE) has to search during itsRI/PCI/PMI computation when it reports channel state information.According to 3GPP standard TS 36.213, a UE is restricted to report PMIand RI within a precoder codebook subset specified by a bitmap parametercodebookSubsetRestriction configured by higher layer signaling (e.g.,RRC layer signaling). For a specific precoder codebook and associatedtransmission mode, the bitmap can specify all possible subsets of theprecoder codebook from which the UE can assume the eNB may be using whenthe UE is configured in the relevant transmission mode. Codebook subsetrestriction is supported for open-loop spatial multiplexing, closed-loopspatial multiplexing, multi-user MIMO and closed-loop rank=1 precoding.The resulting number of bits for each transmission mode is given inTable 1. The bitmap forms the bit sequence a_(A) _(c) ₋₁, . . . , a₃,a₂, a₁, a₀ where a₀ is the LSB and a_(A) _(c) ₋₁ is the MSB and where abit value of zero indicates that the PMI and RI reporting is not allowedto correspond to precoder(s) associated with the bit. The association ofbits to precoders for the relevant transmission modes are given asfollows in Table 3. Hence, it can be seen that the eNB can reduce thecomplexity at the UE in computing the RI/PMI.

TABLE 3 Number of bits A_(C) 2 antenna ports 4 antenna portsTransmission Open-loop spatial 2  4 mode multiplexing Closed-loopspatial 6 64 multiplexing Multi-user MIMO 4 16 Open-loop rank = 1 4 16precoding

FIG. 16 illustrates a flow chart of an example process to implement step1420. In step 1610, the precoder subset provider 1220 may generate aprecoder subset bitmap (e.g., codebookSubsetRestriction bitmap) based onthe precoder subset. Each bit of the precoder subset bitmap correspondsto a precoder element of the codebook. A first value (one or zero) ofeach bit may indicate that CSI reporting is allowed for thecorresponding precoder element, and a second value (the other of one orzero) may indicate that CSI reporting is not allowed for thecorresponding precoder element. For example, of the 16 bitscorresponding to the equivalence capacity rank 4, at most five bits—onebit from each capacity group—may be set to the first value and the restmay be set to the second value. In step 1620, the precoder subsetprovider 1220 may provide the precoder subset bitmap to the receiver120. A layer (e.g., RRC layer) higher than physical layer may be used toprovide the bitmap.

There are many advantages associated with one or more aspects of thedisclosed subject matter. A non-exhaustive list of advantages include:

-   -   Simple to implement;    -   Complexity of RI/PCI or RI/PMI reporting can be reduced without        reducing throughput for one or more ranks;    -   Easily extended to greater number of antennas (e.g., eight) with        large codebook sizes (the advantages become greater).

Although the description above contains many specificities, these shouldnot be construed as limiting the scope of the disclosed subject matterbut as merely providing illustrations of some of the presently preferredembodiments. Therefore, it will be appreciated that the scope of thedisclosed subject matter fully encompasses other embodiments, and thatthe scope is accordingly not to be limited. All structural, andfunctional equivalents to the elements of the above-described preferredembodiment that are known to those of ordinary skill in the art areexpressly incorporated herein by reference and are intended to beencompassed hereby. Moreover, it is not necessary for a device or methodto address each and every problem described herein or sought to besolved by the present technology, for it to be encompassed hereby.

What is claimed is:
 1. A method performed by a receiver to providechannel state information (CSI) as feedback to a transmitter in amulti-antenna wireless communication system, the method comprising:estimating a channel between the transmitter and the receiver;determining a precoder subset comprising one or more precoder elements,each precoder element being a precoder element of a codebook, and theprecoder subset including less than all precoder elements of thecodebook; for each precoder element in the precoder subset, determininga capacity corresponding to that precoder element based on the channelestimation; determining the CSI associated with the precoder elementwhose corresponding capacity is maximum among the capacitiescorresponding to the precoder elements of the precoder subset; andproviding the CSI to the transmitter as the feedback, the CSI comprisinga rank information (RI) and a precoding control index (PCI), wherein thecodebook is defined for a plurality of ranks, wherein for each rank, thecodebook comprises a plurality of precoder elements corresponding tothat rank, wherein at least one rank is an equivalence capacity rank,the precoder elements of each equivalence capacity rank being groupedinto one or more capacity groups in which each precoder element is amember of one capacity group, at least one capacity group includesmultiple precoder elements, and within each capacity group, individualcapacities of the precoder elements of that capacity group are equal,and wherein the step of determining the precoder subset comprises, forat least one equivalence capacity rank, including at most one precoderelement from each capacity group of that equivalence capacity rank intothe precoder subset.
 2. The method of claim 1, wherein for at least oneequivalence capacity rank, the step of including at most one precoderelement from each capacity group comprises including one precoderelement from each capacity group of that equivalence capacity rank intothe precoder subset.
 3. The method of claim 1, wherein for at least oneequivalence capacity rank, the step of including at most one precoderelement from each capacity group comprises any one of: choosing theprecoder element, which is fixed, of that capacity group to be includedin the precoder subset; randomly choosing the precoder element of thatcapacity group to be included in the precoder subset; and receiving theprecoder element of that capacity group to be included in the precodersubset from the transmitter.
 4. The method of claim 1, wherein for atleast one non-equivalence capacity rank above a rank threshold, the stepof determining the precoder subset comprises including less than allprecoder elements of that rank in the precoder subset.
 5. The method ofclaim 1, wherein the multi-antenna wireless communication systemincludes a MIMO system with four transmit antennas, and at least oneequivalence capacity rank is
 4. 6. A non-transitory storage medium whichhas stored therein programming instructions such that when a computerexecutes the programming instructions in a receiver, the computerexecutes the method according to claim 1 to provide channel stateinformation (CSI) as feedback to a transmitter in a multi-antennawireless communication system.
 7. A receiver of a multi-antenna wirelesscommunication system, the receiver structured to provide channel stateinformation (CSI) as feedback to a transmitter, the receiver comprising:a channel estimator structured to estimate a channel between thetransmitter and the receiver; a precoder subset determiner structured todetermine a precoder subset comprising one or more precoder elements,each precoder element being a precoder element of a codebook, and theprecoder subset including less than all precoder elements of thecodebook; a capacity determiner structured to determine, for eachprecoder element in the precoder subset, a capacity corresponding tothat precoder element based on the channel estimation; a channel statedeterminer structured to determine the CSI associated with the precoderelement whose corresponding capacity is maximum among the capacitiescorresponding to the precoder elements of the precoder subset; and afeedback provider structured to provide the CSI to the transmitter asthe feedback, the CSI comprising a rank information (RI) and a precodingcontrol index (PCI), wherein the codebook is defined for a plurality ofranks, wherein for each rank, the codebook comprises a plurality ofprecoder elements corresponding to that rank, wherein at least one rankis an equivalence capacity rank, the precoder elements of eachequivalence capacity rank being grouped into one or more capacity groupsin which each precoder element is a member of one capacity group, atleast one capacity group includes multiple precoder elements of theequivalence capacity rank, and within each capacity group, individualcapacities of the precoder elements of that capacity group are equal,and wherein for at least one equivalence capacity rank, the precodersubset determiner is structured to include at most one precoder elementfrom each capacity group of that equivalence capacity rank into theprecoder subset.
 8. The receiver of claim 7, wherein for at least oneequivalence capacity rank, the precoder subset determiner is structuredto include one precoder element from each capacity group of thatequivalence capacity rank into the precoder subset.
 9. The receiver ofclaim 7, wherein for at least one equivalence capacity rank, theprecoder subset determiner is structured to: choose the precoderelement, which is fixed, of that capacity group to be included in theprecoder subset, randomly choose the precoder element of that capacitygroup to be included in the precoder subset, or receive the precoderelement of that capacity group to be included in the precoder subsetfrom the transmitter.
 10. The receiver of claim 7, wherein for at leastone non-equivalence capacity rank above a rank threshold, the precodersubset determiner is structured to include less than all precoderelements of that rank in the precoder subset.
 11. The receiver of claim7, wherein the multi-antenna wireless communication system includes aMIMO system with four transmit antennas, and at least one equivalencecapacity rank is 4.